       Re: Simplify With Assumptions

• To: mathgroup at smc.vnet.net
• Subject: [mg17963] Re: [mg17931] Simplify With Assumptions
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Mon, 7 Jun 1999 02:51:20 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```This is strange because it is possible to write even in mathematica 3 a
version of simplify which will work with such cases. Here is an very
imperfect example (not meant to be used, there is plenty wrong with it!)
which illustrates the idea:

In:=
<<Algebra`AlgebraicInequalities`

In:=
mysimplify[Sqrt[f_],{vars__},cond_List]:=
PowerExpand[Sqrt[f]]/;SemialgebraicComponents[
Append[cond,
PowerExpand[Sqrt[Denominator[f]]]*PowerExpand[Sqrt[Numerator[f]]]<
0],{vars}]=={};
mysimplify[f_,{vars_},cond_List]:=Simplify[f]

Now we can do not only things like:

In:=
mysimplify[Sqrt[x^2], {x}, {x > 0}]
Out=
x

but also

In:=
mysimplify[Sqrt[(2*t^2 + 1)^2/t^2], {t}, {t > 0}]
Out=
2
1 + 2 t
--------
t

One of the many unsatisfactory things is that

In:=
mysimplify[Sqrt[x^2], {x}, {x < 0}]
Out=
2
Sqrt[x ]

instead of -x, but one could obviously fix that. I can't see any obvious
reason why a (much better) version has not been implemented. Perhaps Adam
Strzebonski would like to comment?

--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: "David Park" <djmp at earthlink.net>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg17963] [mg17931] Simplify With Assumptions
>Date: Sat, Jun 5, 1999, 3:56 PM
>

> Simplify with assumptions in Version 4 is not everything one might
> hope.
>
> Simplify[Sqrt[x^2], x > 0]
> x
>
> But
>
> Simplify[Sqrt[(1 + 2*t^2)^2/t^2], t > 0]
> Sqrt[4 + 1/t^2 + 4*t^2]
>
> not
>
> (1 + 2*t^2)/t
>
> Of course we can see for ourselves and PowerExpand. Yet one would have
> hoped that Mathematica would have handled this case automatically.
>
> David Park